Executive Summary : | General relativity, a successful physical theory, was developed through the interaction between physics and mathematics. It describes the properties of space-time through a metric tensor and an affine connection. General relativity significantly influenced physics, astrophysics, and cosmology. Recent measurements from the Planck satellite and observations of distant supernovae have confirmed the Universe's accelerating expansion, with only 5% baryonic matter and 95% dark energy and dark matter. The dark components model assumes the Universe is filled with these mysterious components.
Modified theories of gravity, such as f(R) gravity, have been proposed to explain the late-time cosmic acceleration of the Universe. This research proposal aims to introduce a systematic investigation of the application of Finsler geometry with modified theories of gravitation, proving its theoretical consistency. The approach will also motivate further extensions of the F(R,T), F(Q,T), F(R,G) type family of theories in a Finsler space as an n-dimensional point space. The study aims to show that the proposed approach predicts de sitter type expansions of the Universe, potentially representing a geometric alternative to dark energy. |